A line passes through #(9 ,8 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-05-17T12:02:20

One such point is #(-4,4)#.

A line that passes through #(9,8)# and #(3,5)# has a slope of

#(5-8)/(3-9)=(-3)/(-6)=1/2#

Hence line parallel to it must also have a slope of #1/2# and as it passes through #(4,8)#, its equation using point slope form is

#(y-8)=1/2(x-4)@

or #2y-16=x-4# or #x-2y+12=0#

Any point on #x-2y+12=0# when joined to point #(4,8)# will give a line parallel to the above.

Say #x=-4# then #-4-2y+12=0# or #y=4#

Hence, one such point is #(-4,4)#.